Problem 82 - College Algebra Essentials

Question

Write each number in scientific notation. $$-3829$$

Step-by-Step Solution

Answer

-3829 in scientific notation is \(-3.829 \times 10^3\).

Step 1: Identify the magnitude

The number given is -3829. In this number, the magnitude part is 3829. It implies four digits, but in scientific notation, we have to represent it in terms of a decimal number between 1 and 10. Hence we need to adjust the decimal point.

Step 2: Move decimal point

In magnitude 3829, there is an implicit decimal point at the end of the number. In order for the number to be between 1 and 10, the decimal point needs to be moved 3 places to the left giving 3.829.

Step 3: Formulate the scientific notation

After moving the decimal point 3 places to the left, we end up with 3.829. To reflect this, the scientific notation of 3829 is \(3.829 \times 10^3\). Don't forget to include the original sign of the number, which gives us \(-3.829 \times 10^3\).